Noncommutative Point Sources

TL;DR

This paper develops a perturbative solution for noncommutative gauge theory representing a point charge and explores its implications for the hydrogen atom, revealing measurable shifts in hyperfine splitting due to noncommutativity.

Contribution

It introduces a novel perturbative method to model noncommutative point sources and applies it to quantum mechanics, showing first-order effects on hydrogen atom spectra.

Findings

Derived a noncommutative point charge solution using the Groenewald-Moyal star product.

Found first-order shifts in hydrogen atom hyperfine splitting due to noncommutativity.

Demonstrated the physical implications of noncommutative geometry in quantum systems.

Abstract

We construct a perturbative solution to classical noncommutative gauge theory on ${\mathbb{R}}^{3}$ minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum mechanics of the noncommutative hydrogen atom gives shifts in the $1S$ hyperfine splitting which are first order in the noncommutativity parameter.